Search results for "General Relativity"
showing 10 items of 1057 documents
Sub-Finsler Geodesics on the Cartan Group
2018
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.
Supermanifolds, symplectic geometry and curvature
2015
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
Numerical study of the transverse stability of the Peregrine solution
2020
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time integration, based on a splitting scheme and an implicit Runge--Kutta method for the linear part, is presented. Secondly, the 1D code is combined with a Fourier spectral method in the transverse variable both for elliptic and hyperbolic NLS equations. As an example we study the transverse stability of the Peregrine solution, an exact solution to the one dimensional nonlinear Schr\"odinger (NLS) equation and thus a $y$-independent solution to the 2D NLS. It is shown that the Peregrine solution is unstable against all…
Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals
2012
Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.
Direct stiffness matrices of BEs in the Galerkin BEM formulation
2001
Abstract In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/ r 2 , r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartz's distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.
Modeling and simulation of an offshore crane
2018
This paper presents a mathematical modeling of a crane system using robot modeling theory as well as the numerical simulation of the dynamics of a crane and a marine craft. The simulations are performed in SimulationX and Matlab Simulink. The simulation platform includes a SimulationX-model of the crane, a realistic model of a marine craft using the Marine Systems Simulator(MSS) and the hydrodynamic sea-keeping calculations (VERES program code). The simulation results show a very good picture of the dynamic behavior of the real crane in offshore environment and verify the validation and effectiveness of the presented modeling approach.
Stochastic response of linear and non-linear systems to α-stable Lévy white noises
2005
Abstract The stochastic response of linear and non-linear systems to external α -stable Levy white noises is investigated. In the literature, a differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed. Approximate CF solutions to the …
Modeling quitessential inflation
2001
We develop general criteria to construct unified frameworks for inflation and quintessence which employ a unique scalar field to drive both. By using such a minimal theoretical framework we avoid having to fine-tune couplings and mass-scales. In particular the initial conditions for quintessence are already fixed at the end of the inflationary epoch. We provide concrete realizations of the method which meet all inflationary and quintessence requirements, such as the COBE normalization and the resulting spectral index n = 0.97, which is in excellent agreement with the latest CMB data.
Cuckoo's Eggs in Neutron Stars: Can LIGO Hear Chirps from the Dark Sector?
2018
We explore in detail the possibility that gravitational wave signals from binary inspirals are affected by a new force that couples only to dark matter particles. We discuss the impact of both the new force acting between the binary partners as well as radiation of the force carrier. We identify numerous constraints on any such scenario, ultimately concluding that observable effects on the dynamics of binary inspirals due to such a force are not possible if the dark matter is accrued during ordinary stellar evolution. Constraints arise from the requirement that the astronomical body be able to collect and bind at small enough radius an adequate number of dark matter particles, from the requ…
What is the final state of a black hole merger?
2018
In this short paper we discuss the possibility of testing the nature of astrophysical black holes using the recently observed black hole mergers. We investigate the possibility that a secondary black hole is created in the merger of two astrophysical black holes and discuss potential astrophysical signatures. We point out that black hole mergers are a possible astrophysical mechanism for the creation of quantum black holes with masses close to the Planck mass.